High-enthalpy crystalline phases of cadmium telluride

Cadmium telluride (CdTe) has been studied using synchrotron powder x-ray diffraction in a diamond anvil cell up to 63 GPa at room temperature combined with density functional calculations. The experiment reveals two pressure-induced structural phase transitions with the following sequence: rocksalt → Cmcm (12 GPa) → post-Cmcm (42 GPa). The crystal structure of the long-sought post-Cmcm phase is characterized. It has a monoclinic unit cell and the P 2 1 / m space group. Calculation conﬁrms this phase transition sequence and further predicts a P 2 1 / m to P 4 / nmm transition near 68 GPa. Interestingly, the enthalpy of CdTe is found to be higher than the enthalpy sum of its constituents Cd and Te at pressures higher than 34 GPa. This suggests that CdTe becomes a high-enthalpy compound at high pressure. Extraordinary dynamic stability revealed in the phonon dispersion relations prevents the decomposition of CdTe at high pressure.


I. INTRODUCTION
Cadmium telluride (CdTe) is a direct-band-gap semiconductor with a band-gap size matching almost perfectly to the solar spectrum [1,2].This trait makes CdTe an optimal material for low-cost high-efficiency photovoltaic applications.Current state-of-the-art CdTe-based single-junction devices can reach a conversion efficiency as high as 22%, providing a low-cost alternative to conventional silicon-based devices [3].Moreover, doped CdTe and variants have numerous applications in thermoelectrics, ferroelectrics, and quantum dots [4][5][6].Driven by its versatile applications, the study of CdTe is currently very active.Since the properties of CdTe are closely tied to its crystal structure, understanding the latter and its changes under external stimuli is a key step to developing new applications.
At ambient conditions, crystalline CdTe adopts the semiconducting zinc-blende structure, which is a common structure for group II-VI binary compounds.Near 3.5 GPa, CdTe transforms into a semimetallic rocksalt structure via an intermediate cinnabar structure which has a very narrow region of stability [7,8].A further transition occurs at 10 GPa to a metallic Cmcm structure [8].The formation of a metallic phase in the Cmcm structure is attributed to the distortion of the structure driven by soft-phonon modes in the transverse acoustic branch [9].A further transition of CdTe was observed at 42 GPa to an unidentified phase (the post-Cmcm phase) [10].Until now, little is known about this phase, except it is stable to at least 55 GPa.Theoretically, the zinc-blende → cinnabar → rocksalt → Cmcm transition sequence and critical pressures were accurately reproduced using density functional theory (DFT)-based calculations [9,11].A phase transition had been predicted at 44 GPa [9], which is in fact very close to the experimental value, but the predicted structure (P − 3m1) clearly does not match the x-ray-diffraction (XRD) pattern of the post-Cmcm phase.Moreover, DFT calculation shows that the enthalpy of CdTe should become higher than that of its elemental constituents (Cd and Te) at 34 GPa, indicating that CdTe may actually undergo an elemental dissociation in this pressure neighborhood [9].
To date, the post-Cmcm phase of CdTe remains unknown and the predicted dissociation in this pressure neighborhood adds to the mystery.To address this problem and understand the mechanisms underlying the interesting phase transitions, we carried out a detailed synchrotron XRD and computational study of CdTe in the rocksalt to post-Cmcm regions (6-63 GPa).Our experiment successfully reproduces the rocksalt to Cmcm transition at 10.5 GPa and the Cmcm to post-Cmcm transition at 42 GPa.The measured XRD pattern for the post-Cmcm phase agrees very well with the previously reported pattern.Using the metadynamics method and Le Bail refinement, we identify the structure of this phase as a monoclinic P2 1 /m structure.The P2 1 /m structure is a distorted form of the B11 structure (P4/nmm) and can be viewed as an intermediate phase for the Cmcm to B11 transition in a broader pressure range.Consistent with previous reports, both P2 1 /m and B11 structures are found to have higher enthalpies than their elemental constituents.This extraordinary phenomenon is attributed to a significant kinetic energy barrier separating crystalline CdTe from elemental phases in composition space.

A. Experimental methods
High-purity commercially available (Sigma-Aldrich greater than 99.9999%) CdTe was grounded to fine powder for the angle dispersive XRD measurements.The sample and pressure sensors (gold and ruby) were loaded into a diamond-anvil cell with neon as a pressure transmitting medium (PTM).A Mar-CCD detector was used at the Advanced Light Source, Lawrence Berkeley National Laboratory Beamline 12.2.2 to collect pressure-dependent XRD data.The x-ray probing beam spot size was focused to approximately 10 μm.Additional details on the XRD experimental setups are given in Ref. [12].Pressure was determined using a known ambient temperature equation of state (EOS) of gold [13] and also calibrated ruby luminescence [14].Integration of powder-diffraction patterns to yield scattering intensity versus 2θ diagrams and initial analysis were performed using the DIOPTAS program [15].Calculated XRD patterns were produced using the POWDER CELL program [16] for the corresponding crystal structures according to the EOSs determined experimentally and theoretically in this study and assuming continuous Debye rings of uniform intensity.Le Bail refinements were performed using the GSAS software [17].Indexing of XRD patterns has been performed using the DICVOL program [18] as implemented in the FULLPROF suite.

B. Computational methods
First-principles metadynamics calculations [19] were performed to simulate the high-pressure phase transitions of CdTe and identify different structures.The simulation has been carried out using the projector augmented plane-wave (PAW) potentials [20,21] and the Vienna ab initio simulation (VASP) program [22].The PAW potentials with the Perdew-Burke-Ernzerhof functional [23] and a 650-eV energy cutoff were used for Cd and Te, which employ 4s 2 4p 6 4d 10 5s 2 and 5s 2 5p 4 as valence states, respectively.The Cmcm structure was used as the starting structure for the simulation at room temperature (300 K) and in the pressure range of 50-120 GPa, using various supercells that consisted of 8-32 CdTe formula units (f.u.) along with a k spacing of 2π × 0.08 Å −1 for the Brillouin zone sampling.Each metastep consisted of a molecular dynamics simulation within the canonical (NV T ) ensemble for a simulation time of 0.8 ps.Enthalpy and electronic structure calculations for candidate structures were conducted using the same PAW potentials and VASP but with a fine k spacing of 2π × 0.03 Å −1 .Phonon calculations were performed using the quantum ESPRESSO package [24] with norm-conserving pseudopotentials and an energy cutoff of 75 Rydberg, along with a 4 × 4 × 4 q-point mesh and an 8 × 8 × 8 k-point mesh.

III. RESULTS AND DISCUSSION
The XRD patterns of the CdTe sample measured at several pressures on pressure increase clearly revealed a series of phase transitions (Fig. 1).At low pressure (6-10.5 GPa), the XRD patterns can be unambiguously indexed to the rocksalt structure.The d spacings of the observed peaks match perfectly a face-centered-cubic lattice.The strongest reflection peak at around 10 • is from the (200) reflection, while the other five peaks are (220), ( 222), (400), (420), and (422).Since Cd and Te have close number of electrons, the (111) reflection by the two elements almost cancels out and therefore appears to be absent.At 12 GPa, the first phase transition takes place, shown by the appearance of additional Bragg peaks.Moreover, the (200) peak splits into three peaks, namely, (020), (200), and (002), corresponding to an orthorhombic distortion.Indexing of the whole XRD pattern revealed that the crystal structure is indeed the Cmcm as previously reported.The Cmcm structure is observed to be stable until at least 42 GPa on pressure increase.
The pressure dependence of the lattice parameters and volumes for the rocksalt and Cmcm structures from 6 to 46 GPa were obtained from the measured d spacings and compared with the calculated values [Figs.2(a) and 2(b)].The onset of the phase transition appears near 12 GPa.In the transition region, all three lattice parameters undergo continuous changes with no obvious discontinuity in unit cell volume, in agreement with a previous study [8].The changes, which are the a-axis decreasing at a rate similar to that for the rocksalt structure and the b-axis increasing and c-axis decreasing at much higher rates, reveal an evolution of the cubic lattice to an orthorhombic lattice.This transition is therefore dictated This transition mechanism is visualized in Fig. 3.In this transition, the sixfold coordination of the rocksalt structure evolves to 5 + 3 coordination in the Cmcm structure.Once the Cmcm structure is fully settled (above 30 GPa), the three lattice parameters decrease all together at about the same rate.The calculation matches very well the experiment for the rocksalt structure and the Cmcm structure at the highpressure end [Fig.2(a)].In the transition region, however, the DFT calculation was not able to reproduce the continuous nature of the transition, instead showing a sudden jump at the transition point.From an experimental perspective it is possible that there are significant internal strains in the sample which can hold the orthorhombic structure at intermediate stages, resulting in a large hysteresis for the phase transition and the coexistence of two phases.The structure optimization calculation, on the other hand, has no constraints on degrees of freedom and therefore can only be settled on the ending structure.The interesting changes of lattice parameters across the rocksalt to Cmcm transition has been observed previously, which caused confusion and led to incorrect identification of the Cmcm structure [28,29].We conducted unweighted fits to the experimental P-V data using a third-order Birch-Murnaghan EOS [25] and determined the bulk modulus B and its first derivative B at the experimental onset pressure for the rocksalt and the Cmcm.The elastic parameters obtained in this way are given in Table I.
The onset of the second phase transition was observed at 46 GPa (Fig. 1).This is also a continuous transition that spans over a course of 7 GPa.The obtained phase is stable to at least 63 GPa, the highest pressure attained in this study.The XRD pattern for the phase (i.e., at 53 GPa) bears a close resemblance to that of the previously reported post-Cmcm phase [10].A careful inspection of the XRD pattern shows that this structure does not belong to any known structures of CdTe and other group II-VI binary compounds.A preliminary indexing of the XRD pattern at 63 GPa shows that it has a P-type monoclinic cell with Z = 4 (f.u. per unit cell).However, this solution is inconclusive without the knowledge of atomic positions in the unit cell.To address the structure, metadynamics calculations were performed to simulate phase transitions starting from the Cmcm structure.The simulation was carried out in a vast pressure region, from 50 to 120 GPa, to capture as many phase transitions as our computation resource can afford.Many structures were found to have competitive enthalpies in this region but with different space groups, i.e., P − 1, C2/m, C2/c, P2 1 /m, P2/m, P2 1 /c, Pbcm, I4/mmm, and P − 3m1.Out of all structures, the one that matches best the experimental XRD pattern of the post-Cmcm phase is the P2 1 /m structure with Z = 4.
Figure 4(a) shows a comparison of the simulated XRD pattern for the P2 1 /m structure to the experimental pattern at 63 GPa.It can be seen that all major reflection peaks and features are well reproduced by this structure.At high 2θ angles (greater than 20 • ), the experimental XRD pattern is degraded because of the reduced diffracted intensity, but the calculation nevertheless reveals several reflections.The experimental XRD pattern is then analyzed by performing Le Bail refinements in order to determine the structural parameters.Preferred orientation effects and strongly anisotropic peak broadening effects, which are usual under high-pressure conditions, prevent a full structural refinement (Rietveld) of the positional parameters.Thus, the theoretically determined positional parameters are used as starting parameters.A typical refined high-pressure pattern is shown in Fig. 4(b).The corresponding structural parameters along with the theoretical values are summarized in Table I.In view of this good match, we suggest the P2 1 /m structure as the structure of the post-Cmcm phase.I. Experimental and calculated structural parameters of rocksalt, Cmcm, and post-Cmcm (P2 1 /m) phases of CdTe at selected pressures: space group (SG), number of formula units in the unit cell Z, lattice parameters, cell volume, bulk modulus B and its pressure derivative B , Wyckoff site, and the corresponding coordinates.Calculated values are presented under the experimental values.B11 structures and the common subgroup for this transition path.In a broader pressure range, the phase transition of CdTe is viewed as a B1 to B11 transition by passing Cmcm and P2 1 /m intermediate phases (Fig. 3).
To examine the energetics, the enthalpies of the Cmcm, P2 1 /m, and B11 structures were calculated at different pressures (Fig. 5).This calculation shows that the P2 1 /m structure becomes thermodynamically more stable than the Cmcm structure near 45 GPa, indeed very close to the experimental transition pressure (46 GPa).The B11 structure is calculated to be more stable than the P2 1 /m structure near 68 GPa.This finding establishes the P2 1 /m structure as the intermediate phase between the Cmcm and P4/nmm structures.Previously, the B2 structure (as in CsCl) was suggested as a candidate structure for the post-Cmcm phase on account of its low Madelung energy, which becomes dominant in determining structures at small volumes [30,31].After all, the B1 to B2 transition has been found in many covalent binaries under high pressure.Our calculation shows that the B2 structure of CdTe indeed becomes more stable than the Cmcm structure near 73 GPa, but is never more stable than the P2 1 /m and B11 structures.The B2 structure therefore does not have a region of stability.In terms of the electronic structure, all four structures were found to be metallic from electronic band and density of states calculations.This agrees with previous observations that CdTe turns metallic in the B1 structure.
The calculated transition sequence in Fig. 5 agrees very well with the experiment.However, an intriguing finding puzzles us, that is, the enthalpy of CdTe is higher than the enthalpy sum of its elemental constituents (Cd and Te) at pressures higher than 34 GPa.In fact, this unusual behavior of CdTe has been pointed out in a previous DFT study [9].From a thermodynamic perspective, this suggests that CdTe is prone to decomposition, but this obviously contradicts the fact that CdTe is stable to at least 63 GPa.A comparison of the experimental patterns of CdTe above 34 GPa with the calculated patterns of Cd (hcp) and Te (bcc) at the same pressures [26,27] definitely rules out the possibility of a decomposition.Interestingly, a similar situation has been found in ZnTe as well, that ZnTe is calculated to dissociate to elemental components at 38 GPa [32], but experiment shows that it is stable to at least up to 85 GPa [10].Although this is somewhat mysterious, it may not be a coincidence but something related to tellurium compounds.To this end, the mechanical and dynamical stabilities of the P2 1 /m and B11 structures are examined by phonon calculations [Figs.6(a) and 6(b)].The absence of the imaginary frequencies in the phonon dispersion confirms that these two structures are dynamically stable.The established dynamical stability ensures that these two structures do not decompose into elements.Thus, the P2 1 /m and B11 phases are metastable high-enthalpy phases.
One contributing factor to this discrepancy is the temperature effects.Our calculations are for the ground states at T = 0 K, so they likely underestimate or overestimate the decomposition pressure, but the errors should be minor since the vibrational free energy is only on the order of 10 meV/atom at room temperature.Moreover, since CdTe, Cd, and Te are all in the solid state at room temperature, there are no large heat reservoirs, i.e., heat of fusion and vaporization, to reverse the huge enthalpy difference between CdTe and the elements.Thus, we speculate that there exists a large kinetic energy barrier for the decomposition of CdTe, which necessitates an activation energy (such as extra pressure or elevated temperature) to overcome it.For example, the high-pressure synthesis of new compounds from elemental constituents, which is the reverse process of decomposition, always requires much higher pressure than what is predicted for the dissociation pressure and most of the time requires increased temperature [33][34][35].
To gain deeper insight into the stability of CdTe at elevated pressures in Fig. 2(b) we compare the atomic volume of CdTe with the experimentally determined [26,27] and the calculated (in this study) volume of the superposition of (Cd + Te)/2 as a function of pressure.As can be clearly seen, the atomic volume of CdTe is always larger than the superposition of (Cd + Te)/2 both below and above the critical pressure for decomposition (34 GPa) as determined by enthalpy calculations.In fact, the atomic volume of CdTe is always larger than that of its constituents even at ambient conditions [36].This observation implies that CdTe has a much lower potential energy (higher stability) than the superposition of (Cd + Te)/2 and provides a plausible explanation for the experimentally observed stability of CdTe at higher pressures.Still, the observed stability of CdTe for more than 30 GPa above the theoretical dissociation point is very significant, and future investigation is encouraged to address this interesting question.

IV. SUMMARY
The high-pressure phase transition of CdTe has been investigated by a combined experimental and computational study up to 63 GPa.The previously reported B1 to Cmcm and Cmcm to post-Cmcm phase transitions were successfully identified by synchrotron XRD measurements.The long-sought crystal structure for the post-Cmcm phase was characterized as a monoclinic P2 1 /m structure.Analysis of the phase transition pathway suggested that the P2 1 /m structure is an intermediate phase between the Cmcm and B11 phases.Using enthalpy calculation, the P2 1 /m to B11 phase transition was predicted to occur near 68 GPa.In the pressure range of interest, the enthalpy of CdTe is constantly higher than the enthalpy sum of Cd and Te, indicating that CdTe is a high-enthalpy compound which is stabilized by a tremendous kinetic barrier.

FIG. 1 .
FIG. 1. Experimental XRD patterns of CdTe at various pressures measured on pressure increase.The XRD patterns of the rocksalt, Cmcm, and post-Cmcm phases are shown by black, red, and blue lines, respectively.The XRD patterns of mixtures of Cmcm and rocksalt and of Cmcm and post-Cmcm (P2 1 /m) phases are shown by yellow and green lines, respectively.

FIG. 2 .
FIG. 2. (a) Pressure dependence of the lattice parameters of CdTe and (b) volume-pressure data for the rocksalt, Cmcm, and post-Cmcm CdTe.Experimental and calculated values are shown with solid symbols and dashed lines, respectively.The solid lines in (b) are unweighted third-order Birch-Murnaghan EOS fits to the experimental data points [25].In (b) the experimental [26,27] and the calculated volume of the superposition of (Cd + Te)/2 are also shown for comparison.

FIG. 3 .
FIG. 3. Transition pathway for the B1 → Cmcm → P2 1 /m phase transition.Shown on the right is the structural relation between B1 and B11 structures.The Cd and Te atoms are colored purple and yellow, respectively.

FIG. 4 .
FIG. 4. (a) Experimental XRD pattern for the post-Cmcm phase at 63 GPa compared with the simulated XRD pattern for the P2 1 /m and P4/nmm structures at the same pressure and (b) Le Bail refinement results for the P2 1 /m structure of CdTe at 63 GPa.Symbols correspond to the measured profile and the red solid lines represent the results of Le Bail refinement.The difference curves (blue curves) are shown also.Vertical ticks mark the positions of the Bragg peaks of the of the P2 1 /m phase of CdTe.The dagger and double dagger mark the locations of Bragg peaks due to Re (gasket) and Ne (PTM), respectively.The asterisk marks a Bragg peak that cannot be explained at the moment.

FIG. 5 .
FIG. 5. Calculated enthalpies for Cmcm, P2 1 /m, P4/nmm, and B2 (CsCl) structures at different pressures.The enthalpy of the Cmcm structure is used as the zero-energy reference.The enthalpy sum for elemental solids Cd and Te is present for comparison.